What is the derivative of (csc(x)/x) ?

The derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)

What is the first derivative of (csc(x)/x) ?

The first derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)

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\frac{d}{d x} (\frac{csc ( x )}{x})

\frac{- x cot ( x ) csc ( x ) - csc ( x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{csc ( x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( csc ( x ) ) x - \frac{d x}{d x} csc ( x )}{x ^{2}}

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

\frac{d x}{d x} = 1

= \frac{( - cot ( x ) csc ( x ) ) x - 1 \cdot csc ( x )}{x ^{2}}

Simplify

= \frac{- x cot ( x ) csc ( x ) - csc ( x )}{x ^{2}}

What is the derivative of (csc(x)/x) ?
The derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)
What is the first derivative of (csc(x)/x) ?
The first derivative of (csc(x)/x) is (-xcot(x)csc(x)-csc(x))/(x^2)